The Italian Domination Number of Graphs Based on Decomposition and Combination Chain Method

Domination on graphs is an important part in Graph Theory. According to different practical application backgrounds, many kinds of domination are presented. Italian domination is a new kind of domination on graphs. To determine the Italian domination number of a graph is a non-deterministic polynomial problem (i.e. NP-hard problem) . In this research, the decomposition and combination chain method in extenics is used to prove that the lower bound of the Italian domination number of a graph is equal to the upper bound, so that the Italian domination number can be determined. The method has good portability and can be used to determine different domination numbers of various graphs.